I found a link to this iPhone app on a Facebook group that I’m a member of. It’s a neat little tool that shows you the closest parkruns to you, their location on the map with travel time and directions. There is even a view course link which takes you off to each runs official parkrun page.
It’s simple to use, allow it to use your location then just update the settings with your barcode number, select the number of events you want to find and whether or not you want to hide ones you’ve already done.
Click on this link to use the tool for yourself.
Edit: there is an offering for Android that allows you to search for runs nearby – click on this link for Android